Neutrino Physics

陆锦标 Kam-Biu Luk Tsinghua University

andUniversity of California, Berkeley

andLawrence Berkeley National Laboratory

Lecture 6, 11 June, 2007

2

Outline

• Neutrino interactions - elastic scattering - inelastic scattering

• Background - cosmic ray - natural radiation - spallation neutron• Reduction of background

3

νe Interactions• νe interacts with atomic electrons: elastic scattering

!

"(#ee$#

ee) =

GF

2s

%

1

2+ sin

2&W

'

( )

*

+ ,

2

+1

3sin

4 &W

-

. /

0

1 2

3 9.5 410545 E#

1MeV

'

( )

*

+ , cm

2

It can take place at any energy.

νe + e- → νe + e-

!

sin2"

W= 0.23

GF = Fermi constant

=1.167x10-5 GeV-2

ν eeν

4

νe Interactions• νe interactions with atomic electrons: elastic scattering

!

"(# ee$#

ee) =

GF

2s

%

1

3

1

2+ sin

2&W

'

( )

*

+ ,

2

+ sin4 &

W

-

. /

0

1 2

3 4.0 410545 E#

1MeV

'

( )

*

+ , cm

2

It can also take place at any energy.

νe + e- → νe + e-

νe νe

e- e-

Z0

e-

W-

νeνe

e-

5

νµ Interactions• νµ interactions with atomic electrons: elastic scattering

!

"(# µe$# µe) =G

F

2s

%

1

2& sin

2'W

(

) *

+

, -

2

+1

3sin

4 'W

.

/ 0

1

2 3

41.6 510&45 E#

1MeV

(

) *

+

, - cm

2

νµ + e- → νµ + e-

νµ νµ

e- e-

Z0 W+

νµ

e-

e-

νµ

6

νµ Interactions• νµ interactions with atomic electrons: elastic scattering

!

"(# µe$# µe) =G

F

2s

%

1

3

1

2& sin

2'W

(

) *

+

, -

2

+ sin4 '

W

.

/ 0

1

2 3

41.3510&45 E#

1MeV

(

) *

+

, - cm

2

νµ + e- → νµ + e-

νµ νµ

e- e-

Z0

7

Inelastic νµ Interactions• νµ interactions with atomic electrons:

!

"(# µe$# eµ) =GF

2

%

s&mµ

2( )2

s for low energies

=GF

2s

% for high energies

'17 (10&45 E#

1MeV

)

* +

,

- . cm

2

νµ + e- → νe + µ-

W+

νµ

e-

µ-

νe

8

Inelastic νe Interactions• νe interactions with atomic electrons:

µ-

W-

νµνe

e-

νe + e- → νµ + µ-

!

"(# µe$# eµ) =GF

2

3%

s&mµ

2( )2

s for low energies

=GF

2s

3% for high energies

' 5.7 (10&45 E#

1MeV

)

* +

,

- . cm

2

9

Tau Neutrino Interactions

The cross sections of ντ and ντ with electron are identical

to those of the muon neutrinos.

10

Neutrino-nucleon Interactionsνe + n → e- + p

ν pe-

n

dud

duu

W-

e-νe

In the laboratory,

For less than 1 GeV,

!

"(# en$ e%

+ p) =GF

2E#

2(hc)

2

&(gV

2+ 3gA

2) 1+

Q

E#

'

( )

*

+ , 1+ 2

Q

E#

+Q

2 %me

2

E#2

= 9.3-10%44 E#

1MeV

'

( )

*

+ ,

2

1+Q

E#

'

( )

*

+ , 1+ 2

Q

E#

+Q

2 %me

2

E#2

cm2

where gv = 1, vector coupling constant, gA = 1.23, axial-vector coupling constant, Q = mn - mp = 1.3 MeV

11

Neutral-current Interaction With Nucleon

12

Antineutrino-nucleon Interactions

νe + p → e+ + nInverse beta-decay reaction:

In the laboratory,

pνe+

n

For less than 1 GeV,

!

"(# e p$ e+

+ n) =GF

2E#

2(hc)

2

%(gV

2+ 3gA

2) 1&

Q

E#

'

( )

*

+ , 1& 2

Q

E#

+Q

2 &me

2

E#2

-(E# &Q)

= 9.3.10&44 E#

1MeV

'

( )

*

+ ,

2

1&Q

E#

'

( )

*

+ , 1& 2

Q

E#

+Q

2 &me

2

E#2

-(E# &Q) cm2

where θ(Eν-Q) = 1, for Eν > Q threshold function

= 0, for Eν < Q

13

Cross Sections Of Low-energy ν Scattering

14

Interactions With Nucleons At High-energy• For 50 GeV < Eν < 350 GeV, the inelastic cross sections are:

!

"(#lN$ l

%+ X) & 6.7 '10

%39 E#

GeV

(

) *

+

, - cm

2

!

"(# lN$ l

++ X) % 3.4 &10

'39 E#

GeV

(

) *

+

, - cm

2

15

How Many Neutrino Events?For observing solar neutrino events with the electrons in the water molecule as the targets

Ndet = σνe•Φν•Ntgt

where Φν = 7 x 1010 cm-2s-1,

σνe ~ 10-45 cm2

For the target, the number of electrons in 1 mole of H2O:

(6 x 1023 molecules) x 18 e-/molecule ~ 1025 e-

If 1000 tonne of water is used, then the number of e- is

Ntgt = (103 x 103 x 103/18) x 1025 ~ 1032

Thus, the event rate is: Ndet ~ 0.01 s-1 or 1000 per day !!

16

Dark Side Of Cosmic Ray• At sea level, the intensity of cosmic ray is ~1 cm-2min-1, and has an angular distribution given by

!

dI

dcos"= I

0cos

2"

Most are muons with an average energy of ~4 GeV.

µ- > 1 GeV

• Muons can ionize the target along their path, and can emit Cherenkov photons:

µ− + N → µ− + N+ + e-

or µ− + N → n + X µ− + N → N1 + X

→ N2 + β + νe

which can mimic the neutrino reactions.

• For a 1000 t water cube at sea level, the number of muons going through is ~(10 x 100)2 x 1 min-1 = 1.7 x 104s-1

17

Go Underground

Muons lose energy as they go through rock. Hence they getattenuated.

10-13

10-11

10�-9

10-7

10-5

10-3

10 -1

0 1000 2000 3000 4000 5000 6000 7000 8000

Muon FluxNeutron ProductionMuon Flux

(cm-2 s-1)

Neutron Production(g-1s-1)

Boul

by

Soud

an

Gra

n Sa

sso

Kam

ioka

Frej

us

Mon

t Bla

nc

Sudb

ury

m.w.e.

1 m of granitic rock ≈ 2.6 m of water = 2.6 m.w.e.

metre waterequivalent

18

Natural Radioactivity• The common radioactive isotopes in the environment are:

Gamma rays from 238U, 232Th, and 40K chains

19

More Headache Due To Radioactivity• All materials used in the detector potentially can have natural radioactivity as well, for example, for a low background photomultiplier tube:

2530170Plastic

0300Metal

207030Ceremic

303060Glass

238U (ppb)*232TH (ppb)*40K (ppm)*

* Mass of radioactive nuclide/mass of the material• The number of gamma rays emitted is:

1 mg of natural K gives 285 γ/day with Eγ > 0.1 MeV1 µg of Th gives 958 γ/day with Eγ > 0.1 MeV1 µ g of U gives 2310 γ/day with Eγ > 0.1 MeV

20

Problem With Background Gamma Rays

photon

Atomicelectron

λθ

λ’

• Since the energies of many of the gamma rays from natural radioactivity are more than 1 MeV, they can Compton-scatter to give energetic electrons:

• The electrons can look like those coming from ν or ν interactions.

• A gamma ray could also combine with a low-energy n to appear as a inverse beta-decay event (gamma ray looks like e+ as far as the detector is concerned).

21

Beating Down The Background• The intensity of radiation after passing through a thickness x of material is given by:

!

I(x) = I0e"x /#

where I0 is the initial intensity, λ is the absorption length (for photon, this is also called radiation length)

!

" cm[ ] =

"g

cm2

#

$ % &

' (

)g

cm3

#

$ % &

' (

22

Beating Down The Background (cont.)• The other background is the neutrons produced by muons.• Neutrons can be attenuated with hydrogen-rich materials, e.g. water, paraffin, borated polyethylene.• If water, cheap and easily available, is used:

Neutron absorption vs thickness of water

Fast

neu

tron

s pe

r da

y

water thickness (m)

0.05

0.10

0.15

0.20

0.25

0.30

0. 1. 2.

23

Shielding Neutrino Detector ForNon-accelerator Experiments

targetvolume

buffer

shield

detector

24

Summary• Neutrino interactions have small cross sections at low energies, hence, low event rate.

• Cosmic ray and natural radioactivity are major background in non-accelerator neutrino experiments

• Need large, clean, and well-shielded detectors placed underground to reduce unwanted events